176 



SCIENCE. 



[N. S. Vol. XXIII. No. 579. 



capacity of the water molecules associated 

 with it and that of the same molecules 

 when free. The C is a similar quantity 

 referring to the dissociated ions. 



The formula may most easily be tested 

 in the iona H=W -}- A-\- Bp, when 

 B = C — A. "We may determine the dis- 

 sociation factor from Kohlrausch's values 

 of the electrical conductivities. Testing 

 the formula for those solutions for which 

 Thomsen and Kohlrausch furnish sufficient 

 data, we find that it reproduces the ob- 

 served heat capacities exceedingly well. It 

 breaks down sometimes for concentrations 

 so high as to contain one gram-molecule of 

 the solute to 20 of water. 



The formula obtains additional credit 

 from the circumstance that a precisely sim- 

 ilar formula gives excellent reproductions 

 of the observed volumes of solutions ; these 

 volumes being also additive qi^antities. 



In the cases examined, the constant A is 

 positive, the constant B, negative, and the 

 constant C ^A -\- B, also negative. 



Sodium chloride NaCl 



Potassium chloride KCl 



Sodium hydroxide NaOH 



Potassium hydroxide I KOH 



Ammonium chloride NH^Cl 



Hydrochloric acid HCl 



Sulphuric acid HjSOj 



Magnesium sulphate I MgSOj 



39 

 97 

 32 

 59 

 39 

 3.6 

 37 

 24 



31 



55 

 33 

 51 

 23 

 36 

 43 

 261 



If this conception of a solution is ad- 

 mitted, it leads to the view that the element 

 of the solute is associated with several, at 

 least with more than one, molecules of 

 water. This is not in agreement with the 

 hypothesis made by Traube and by Poyn- 

 ting, by which they have explained the laws 

 of osmotic pressure by means of molecular 

 attractions. They suppose that one, and 

 but one, molecule of water is intimately 

 bound with the molecule or the ion of the 

 solute. We can examine this hypothesis 

 by means of the values obtained for C. 

 This constant represents the sum of the 



heat capacities of the ions of a molecule 

 and of the difference between the heat 

 capacity of the water molecules attached 

 to the ions and their heat capacity when 

 free. We may express this by writing 

 C = a + a(<^ — s), in which a is the heat 

 capacity of the ions, a the number of water 

 molecules in the aggregations around the 

 ions, and 4> and s the two heat capacities 

 of one water molecule. The values of C 

 are all negative and whether we know the 

 value of a or not, it is certainly positive, 

 and not less than that corresponding to 

 the translational degrees of freedom of the 

 ions, or 6 for a solute that splits into 2 ions. 

 Then a(<^ — s) is surely negative and 

 numerically as great as C + 6. If we set 

 a:^2, as Traube 's and Poynting's theories 

 call for in the case of such solutions as 

 those of sodium chloride and hydrochloric 

 acid, we find, from the values of C, that 

 <^ — s is negative, and numerically equal to 

 or greater than 18. But s is equal to 18, 

 the heat capacity of a gram-molecule of 

 water, and we are led to the conclusion 

 that <^ is zero or negative ; that is, that the 

 heat capacity of the water molecules united 

 with the ions disappears entirely or be- 

 comes negative. This result is evidently 

 inadmissible, and I am forced to believe 

 that more than one molecule of water, in 

 all probability several molecules, are asso- 

 ciated with each ion. 



One serious objection may be raised 

 against this conception, namely, that if it 

 were true the molecular conductivities of 

 all binary electrolytes ought to be nearly 

 the same ; for the natural supposition is 

 that the molecular aggregates are pushed 

 by the electric force, and whatever the ions 

 at their centers may be, they all contain 

 about the same number of water molecules, 

 so that they will experience about the 

 same frictional resistance to their motion, 

 and will move at about the same rate. We 

 may evade this objection by considering 



